I would counter many people here, and say influence is not that useful. Of course it has everything to do with the hands you're dealt.
It is fairly simple to play until 1630 without any unmanagable coalitions forming, because when you get an impressive ally like France or Ottomans, no one will touch you, as long as you don't go too crazy, and split the AE on all your borders. Negates the AE bonus from INF
As for the vassal feeding strategy, once absolutism hit, you can easily get >80 absolutism by 1630. Now, coring costs are dirt cheap, even without RCC ideas, and it is way cheaper and much less time consuming to just core everything yourself. Not to mention the pain of dealing with AI's: 1) liberty desire 2) incompetence of AI to keep its realm together. It is during this time the bulk of your territorial expansion happens anyways.
I would nix influence.
Defensive + Religious + Quantity + Admin + w.e. you want. Stack military ideas for the rest of the game.
-50% unjustified demands and a more efficient bird --> paper mana conversion put influence in top 4 easily. The AE savings are gravy, same with useful diprep/extra relations slot (which DIP also gives and one should usually take both in SP). Absolutism reduces dipannex cost too, not just core cost. With enough modifiers annexing a 1000 development vassal takes < 15 years.
The main advantage is to give them all the OE > 100% rather than yourself. Their troops suck, and by extension so do their rebels. If you have >200% OE, you get rebel sentiment galore and get huge rebel stacks all over the world. If you give a client state 400% OE, it vomits out rebels of every type in short order...but all in one clumped area near that front and easily beaten.
Let's not get ahead of ourselves - Espionage is still in the game
In games where you don't need exploration, espionage is a respectable 7th idea group choice for the diplomat. Having 5 allows you to double improve + double annex while still declaring wars which is nice for QoL. Considering how hot garbage the expansion set is, I place espionage comfortably above it, despite that espionage isn't very good.
The handicaps he mentioned are real. You can pick anything, but to justify one option as superior to another you'd need to address the handicaps. Most religions can't keep up conversions with expansion pace, forcing unity policies to maintain absolutism and necessarily enduring more rebels than humanist.
Does declaring offensively into a coalition remove the coalition war enthusiasm modifier? I can see it in that case working.
Yes, there is no "coalition war" modifier if you declare on a coalition. Members are also not considered cobelligerent, despite that the pre-war screen says they will be.
This has been the case for years now and it's objectively bugged (I've reported it ~5 times or so) because the UI and what happens don't align. Regardless, unless it got stealth-changed in 1.23 (not likely) you can trivially break coalitions by setting an OPM as the war leader and assaulting it down to kill enthusiasm. This still costs time and is less optimal than avoiding the coalition via declaring all the wars/being too strong/chaining truces, but it's an option if your timing is off.